Problem Set 1. Use the set of ordered pairs below to answer each question. {(4,20), (8,4),(2,3), (15,3), (6,15),(6,30), (1,5),(6,18),(0,3)} a. Write the ordered pair(s) whose first and second coordinate have a greatest common factor of 3. b. Write the ordered pair(s) whose first coordinate is a factor of its second coordinate. c. Write the ordered pair(s) whose second coordinate is a prime number.

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Question:

Problem Set
1. Use the set of ordered pairs below to answer each question.
{(4,20), (8,4),(2,3), (15,3), (6,15),(6,30), (1,5),(6,18),(0,3)}
a. Write the ordered pair(s) whose first and second coordinate have a greatest common factor of 3.
b. Write the ordered pair(s) whose first coordinate is a factor of its second coordinate.
c. Write the ordered pair(s) whose second coordinate is a prime number.

Answers

a) (15, 3) and (6, 15) and (0, 3) are the ordered pairs whose first and second coordinate have a greatest common factor of 3b) The ordered pair(s) whose first coordinate is a factor of its second coordinate are (4, 20) and (6, 30) and (1, 5) and (6, 18)c) (2 , 3) and (15, 3) and (1, 5) and (0, 3) are ordered pair(s) whose second coordinate is a prime numbersSolution:Given that,Use the set of ordered pairs below to answer each question. {(4, 20),  (8, 4), (2, 3), (15, 3), (6, 15), (6, 30), (1, 5), (6, 18), (0, 3)}a. Write the ordered pair(s) whose first and second coordinate have a greatest common factor of 3So we must find GCF of the ordered pairsGCF of 4 and 20:The factors of 4 are: 1, 2, 4 The factors of 20 are: 1, 2, 4, 5, 10, 20 Then the greatest common factor is 4GCF of 8 and 4:The factors of 4 are: 1, 2, 4 The factors of 8 are: 1, 2, 4, 8 Then the greatest common factor is 4GCF of 2 and 3:The factors of 2 are: 1, 2 The factors of 3 are: 1, 3 Then the greatest common factor is 1GCF of 15 and 3:The factors of 3 are: 1, 3 The factors of 15 are: 1, 3, 5, 15 Then the greatest common factor is 3GCF of 6 and 15:The factors of 6 are: 1, 2, 3, 6 The factors of 15 are: 1, 3, 5, 15 Then the greatest common factor is 3GCF of 6 and 30:The factors of 6 are: 1, 2, 3, 6 The factors of 30 are: 1, 2, 3, 5, 6, 10, 15, 30 Then the greatest common factor is 6GCF of 1 and 5:The factors of 1 are: 1 The factors of 5 are: 1, 5 Then the greatest common factor is 1GCF of 6 and 18:The factors of 6 are: 1, 2, 3, 6 The factors of 18 are: 1, 2, 3, 6, 9, 18 Then the greatest common factor is 6GCF of 0 and 3:The factors of 0 are: All Whole Numbers The factors of 3 are: 1, 3 Then the greatest common factor is 3Summarizing the results:(15, 3) and (6, 15) and (0, 3) are the ordered pairs whose first and second coordinate have a greatest common factor of 3b. Write the ordered pair(s) whose first coordinate is a factor of its second coordinate.So let us find the factors of second cordinate and checkFor (4, 20) , the factors of 20 are 1, 2, 4, 5, 10, 20Thus first coordinate 4 is factor of second cordinateFor (8, 4) the factors of 4 are 1, 2, 4Thus first coordinate is not a factor of second cordinateFor (2, 3), the factors of 3 are 1, 3Thus first coordinate is not a factor of second cordinateFor (15, 3), the factors of 3 are 1 and 3Thus first coordinate is not a factor of second cordinateFor (6, 15) , the factors of 15 are 1, 3, 5, 15Thus first coordinate is not a factor of second cordinateFor (6, 30), the factors of 30 are 1, 2, 3, 5, 6, 10, 15, 30Thus first coordinate 6 is factor of second cordinateFor (1, 5) , the factors of 5 are 1 and 5Thus first coordinate 1 is a factor of second cordinateFor (6, 18) , the factors of 18 are 1, 2, 3, 6, 9, 18Thus first coordinate 6 is factor of second cordinateFor (0, 3) , the factors of 3 are 1 and 3Thus first coordinate is not a factor of second cordinateSummarizing the results:The ordered pair(s) whose first coordinate is a factor of its second coordinate are (4, 20) and (6, 30) and (1, 5) and (6, 18)c. Write the ordered pair(s) whose second coordinate is a prime number.A prime number is a whole number greater than 1 whose only factors are 1 and itself. A factor is a whole numbers that can be divided evenly into another number. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29. Therefore,(2 , 3) and (15, 3) and (1, 5) and (0, 3) are ordered pair(s) whose second coordinate is a prime numbers

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